{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

p1spring08_l

# p1spring08_l - Math 2930 Spring 08 Prelim 1 1 Given the...

This preview shows pages 1–2. Sign up to view the full content.

Math 2930 Spring 08 Prelim 1 1. Given the following differential equation dy dx = 4 x - 2 y, y (0) = 0 (1) (a) Use Euler’s method to approximate the differential equation on the interval x = [0 , 2]. Use a step size of h = 1 / 2 and clearly state any equations used. (b) Solve the differential equation dy dx = 4 x - 2 y , y (0) = 0. (c) What is the error is Euler’s method for y (2) in part (a)? 2. The population of a duck pond is governed by the following differential equation dP dt = 2 P (4 - P ) , P (0) = 2 (2) (a) Solve for the population as a function of time, P ( t ). (b) What is the limiting population? 3. Find the general solution to the differential equation dy dx = x + 2 y y - 2 x (3) For what initial conditions (if any) is the solution guaranteed to exist and be unique? 4. Given the differential equation below, answer the questions. dy dx = ( y - 1)(2 - y )( y - r ) (4) (a) Calculate, then draw the bifurcation diagram for the system. (b) Determine the stability of the critical points (equilibrium curves) in the bifurcation diagram.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

p1spring08_l - Math 2930 Spring 08 Prelim 1 1 Given the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online